Perhaps mathematical maturity has many of the same components as psychological
maturity - namely an ability not to get fazed by minor setbacks and to step back
and see through the trees to the shape of the forest as a whole. This also makes
it easier to recognize parallels between different areas, and a lot of what we
consider creative involves applying an old idea in a new context. So in fact I
think Craig's exception (cited below) is closer to being the rule, and
intuition often is based on the recognition (perhaps not consciously) of a
parallel to some other experience which may or may not have ever been formally
expressed in mathematical terms.

On Aug 4 2004, Craig wrote:
> ....
> I agree with Moursund that math
> intuition can't be a result of applying the same solution technique
> as a result of repetition... except for, possibly, the "repetition"
> of making quick connections to earlier problem solving skills and
> experiences. From that standpoint, having the intuitor explain will
> also build on that "success base," furthering chance of "intuition"
> in a later setting.

This material is based upon work supported by the
National Science Foundation under Grant DUE-0226284.
Any opinions, findings, and conclusions or recommendations
expressed in this material are those of the author(s)
and do not necessarily reflect the views of the
National Science Foundation.